Conversation

Sep 19, 2020

i'm going to bed but let's try and set up a game 1. reply with an interest, a picture, a quote, whatever – something random that you'd like to talk about with someone. ask a question, state an observation 2. reply to someone else in the replies enjoy your new friends

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QC (in Berlin 7/29-??? w/ COVID

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@QiaochuYuan

Sep 20, 2020

anyone wanna talk about how applying the central limit theorem to a random walk in 2D reproduces the euclidean metric starting from a *grid* it’s fucked up and wrong and i’m still trying to figure out what it means

Yoni

@YSvechinsky

Sep 20, 2020

Intuitively to me, it stems from the idea that infinitesimal steps on a grid can approximate any curve So when applying the central limit theorem random walk on a grid approximates random walk in any direction

QC (in Berlin 7/29-??? w/ COVID

Replying to

and

yeah that’s all fine, what’s super weird is the notion of *distance* you get. the natural notion of distance on a grid is “manhattan distance,” the length of the shortest grid path between two points, which is *not* the usual euclidean distance

6:06 PM · Sep 20, 2020Twitter for iPad

QC (in Berlin 7/29-??? w/ COVID

Replying to

and

but what CLT says is if you take two points on the grid very far away from each other and calculate the probability that a long random walk starting at one point ends up at the other, asymptotically that probability is a function of the *euclidean* distance between them! wild!!

Yoni

@YSvechinsky

Sep 20, 2020

Does this work on any grid or only on one that's equally spaced? I think it's interesting because there is a notion of "natural distance" of a certain space that's arising Though again in this specific case it just reminds me of taking infitisimal steps on a curve

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